Question

3. A cubical Gaussian surface encloses a net charge. Each edge of the cube has length 4.0 m. The cube is drawn such that four of its six faces are parallel to the z direction. The net electric field is such that the electric field lines skim each of these four faces. On the top face, the electric field ?⃗⃗ ? = +25?̂ N/C and on the other face ?⃗⃗ ? = −40?̂ N/C. Sketch the cubical Gaussian surface, indicating the z direction, ?⃗⃗ ? and ?⃗⃗

a. Determine the net charge the Gaussian surface encloses. b) Would any of your calculations be affected if you used a spherical Gaussian surface instead of a cubical one? Justify your answer.

Answer 1

see the diagram :

E1 = Et = +25? N/C

E2 = ?_b = −40? N/C

The blue plane is the charged plate (assumed)

the area vector of upper surface is upward and electric field through this surface is also upward.

the area vector of bottom surface is downward and electric field through this surface is also downward.

therefore, flux through both surface is positve.

electric flux = dot product of electric field and area vector.

a) total flux through the cube is [here ]

therefore, according to Gauss's Law :

charge enclosed is equal to = Q = [answer]

b) Yes, the calculations would be affected if we use a spherical Gaussian surface instead of a cubical one. Because, the cross-section area of circle is different from crossection area of cube.

that is, the area enclosed is different, so , charge enclosed is will be different.